Exercise 1. (6 marks) Adeline and Bani are a team in a consulting firm. Once a task is assigned, Adeline first decides whether to work separately (S) or work together (7). Subsequently, Adeline and Bani choose their effort levels. We assume that effort choices are made separately but simultaneously. Let ea and en denote the level of effort exerted by Adeline and Bani respectively where e; E (0, 1} and i = a, b. If Adeline chooses S, each individual i's payoff is Ui = _citei 2 - ei. If Adeline chooses T Uj = uminlei, ejl - ei, where i, j E (a, b} but j # i 2 and minte;, e;) = e; if e; se; and mine;, e;) = e; if e; zej Assume v equals the largest digit in your student ID. (i) (2 marks) Suppose Adeline chooses S. Consider the subgame associated with that choice (i.e. the one that arise following S). . Write the corresponding payoff matrix. . Identify all pure strategy Nash equilibria. . Is there a Nash equilibrium in mixed strategies where at least one player chooses both effort levels with strictly positive probability? Explain. (ii) (2 marks) Suppose Adeline chooses T. Consider the subgame associated with that choice (i.e. the one that arise following 7) and answer the three questions stated in part (i). (iii) (2 marks) Now consider the entire game . Identify a pure strategy profile that is a Subgame Perfect Nash equilbrium (SPNE). Explain why it is SPNE. . Identify a pure strategy profile that is a Nash equilbrium (NE) but not SPNE. Explain why it is a NE but not SPNE. Note: The function minja, b} refers to minimum of two numbers a and b. For example, min(3, 4) = 3; min(3, 1} = 1. In the first case, i.e. between 3 and 4, 3 is minimum. In the second case, i.e., between 3 and 1, 1 is minimum. So minimum of a and b is a when a s b, and minimum of a and b is b when b S a.Exercise 2. (6 marks) Little Italy has 100 consumers all of whom buy either one pizza or nothing. Each consumer has a reservation price of $15. That is, each consumer is willing to pay at most $15 for a pizza. There are two pizza stores - A and B - located next to each other. It costs $1 to make a pizza. Let pa and pb denote the price charged by stores A and B respectively. For simplicity, assume ,0,- e {12, 15} for both 1' : A, B. Hereafter we ignore the dollar sign. Thus, prices can take just one of the two values 12 or 15. If p;